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Proof step 77 from proof compat-put (previous step)

st[r0 -- _type] = typeval(mkclasstype(class0)), sk .fs = mkfs(class1, ty0, fieldvar0), class+∃(str, class0), compatfields(str, r0, instfields(class0), st), r0 ∈ st, r0 -- _type ∈ st, r0 ∈ st[r -- mkfs(class, ty, fieldvar) ', val], r0 -- _type ∈ st[r -- mkfs(class, ty, fieldvar) ', val], compatmode(str, st), compatstatic(str, st), compat(str, val, ty, st), sk ∈ instfields(class0) ⊦ mkfs(class, ty, fieldvar) ' = _length, ty = void_type, r0 = jvmref, r0 -- sk ∈ st, r0 = r ∧ sk = mkfs(class, ty, fieldvar) '

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 75:
⊦ compatfields(str, r, sks, st) ↔ (∀ sk. sk ∈ sks → r -- sk ∈ st ∧ is_fskey(sk) ∧ compat(str, st[r -- sk], sk .fs .type, st))
Proof step 76:
st[r0 -- _type] = typeval(mkclasstype(class0)), sk .fs = mkfs(class1, ty0, fieldvar0), class+∃(str, class0), ∀ sk. sk ∈ instfields(class0) → r0 -- sk ∈ st ∧ is_fskey(sk) ∧ compat(str, st[r0 -- sk], sk .fs .type, st), r0 ∈ st, r0 -- _type ∈ st, r0 ∈ st[r -- mkfs(class, ty, fieldvar) ', val], r0 -- _type ∈ st[r -- mkfs(class, ty, fieldvar) ', val], compatmode(str, st), compatstatic(str, st), compat(str, val, ty, st), sk ∈ instfields(class0) ⊦ mkfs(class, ty, fieldvar) ' = _length, ty = void_type, r0 = jvmref, r0 -- sk ∈ st, r0 = r ∧ sk = mkfs(class, ty, fieldvar) '

Rule argument

[crewrite-arg: fields-compat , F , [st, sks, r, str] → [st, instfields(class0), r0, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, instfields(class0), r0, str)]]